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Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up technique of singularities

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  • It is a big problem to distinguish between integrable and non-integrable Hamiltonian systems. We provide a new approach to prove the non-integrability of homogeneous Hamiltonian systems with two degrees of freedom. The homogeneous degree can be taken from real values (not necessarily integer). The proof is based on the blowing-up theory which McGehee established in the collinear three-body problem. We also compare our result with Molares-Ramis theory which is the strongest theory in this field.
    Mathematics Subject Classification: Primary: 37J30; Secondary: 70F16.


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